Nonlinear Tearing Mode Interactions and Mode Locking in Reversed Field Pinches, C.C. Hegna, Center for Plasma Theory and Computation Report UW-CPTC 96-3.

The nonlinear interaction of a set of tearing instabilities and plasma flow is studied in a cylindrical plasma. An analytic theory of mode locking is developed which includes the effects of the localized electromagnetic torques, plasma inertia and cross-field viscosity. The calculation is specialized for the case of mode locking on the Madison Symmetric Torus (MST) reversed field pinch. In MST plasmas, a set of m=1 tearing instabilities becomes phase locked and forms a toroidally localized, rotating magnetic disturbance. An evolution equation for the phase velocity of this magnetic disturbance is derived which accounts for two types of electromagnetic torques. The external torques describe the interaction of the tearing modes with static magnetic perturbations locked outside the plasma region. The interior torques describe the nonlienar interaction of three tearing modes which satisfy a wave number resonance condition. For conditions typical of MST, the internal torques dominate the external torques, which suggests that the nonlinear interaction of tearing instabilities plays a prominent role in the momentum degradation and mode locking.